Orienting transversals and transition polynomials of multimatroids

Multimatroids generalize matroids, delta-matroids, and isotropic systems, and transition polynomials of multimatroids subsume various polynomials for these latter combinatorial structures, such as the interlace polynomial and the Tutte-Martin polynomial. We prove evaluations of the Tutte-Martin polynomial of isotropic systems from Bouchet directly and more efficiently in the context of transition polynomials of multimatroids. Moreover, we generalize some related evaluations of the transition polynomial of 4-regular graphs from Jaeger to multimatroids. These evaluations are obtained in a uniform and matroid-theoretic way. We also translate the evaluations in terms of the interlace polynomial of graphs. Finally, we give an excluded-minor theorem for the class of binary tight 3-matroids (a subclass of multimatroids) based on the excluded-minor theorem for the class of binary delta-matroids from Bouchet. (C) 2017 Elsevier Inc. All rights reserved.

Publication year:2018

Keywords:multimatroid, isotropic system, transition polynomial, tutte polynomial, interlace polynomial, matroid, 4-Regular graph

BOF-keylabel:yes

IOF-keylabel:yes

BOF-publication weight:1

CSS-citation score:1

Authors from:Government, Higher Education, Private

Accessibility:Open